{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NTA2ZQVL2IBFCO4ENHP2CZT7PZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c15c95268fc0dc9edd03e7fa75195302868e732b555fffd3427c9a2d8689318e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-28T20:58:56Z","title_canon_sha256":"d9b59dcea8ed68c9440d0d5501e3ba4977e4f3a4d5cc9f35cc5190fa77345fc6"},"schema_version":"1.0","source":{"id":"1811.11830","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11830","created_at":"2026-05-17T23:54:33Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11830v2","created_at":"2026-05-17T23:54:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11830","created_at":"2026-05-17T23:54:33Z"},{"alias_kind":"pith_short_12","alias_value":"NTA2ZQVL2IBF","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NTA2ZQVL2IBFCO4E","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NTA2ZQVL","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:3cc02cd78b1b0332c6b2d0c7b9eeb1275d589f57ce727ef04db39e46b54fe0d8","target":"graph","created_at":"2026-05-17T23:54:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the invariants (in particular, the central invariants) of suitable Poisson pencils from the point of view of the theory of bi-Hamiltonian reduction, paying a particular attention to the case where the Poisson pencil is exact. We show that the exactness is preserved by the reduction. In the Drinfeld-Sokolov case, the same is true for the characteristic polynomial of the pencil, which plays a crucial role in the definition of the central invariants. We also discuss the bi-Hamiltonian structures of a generalized Drinfeld-Sokolov hierarchy and of the Camassa-Holm equation.","authors_text":"Andrea Raimondo, Marco Pedroni, Paolo Lorenzoni","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-28T20:58:56Z","title":"Poisson pencils: reduction, exactness, and invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11830","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:133bbf67c406054c66f189240e2f3b4b7e7303bdf3e2d76a3353da3a074ac53d","target":"record","created_at":"2026-05-17T23:54:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c15c95268fc0dc9edd03e7fa75195302868e732b555fffd3427c9a2d8689318e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-28T20:58:56Z","title_canon_sha256":"d9b59dcea8ed68c9440d0d5501e3ba4977e4f3a4d5cc9f35cc5190fa77345fc6"},"schema_version":"1.0","source":{"id":"1811.11830","kind":"arxiv","version":2}},"canonical_sha256":"6cc1acc2abd202513b8469dfa1667f7e6e10443a14edcd60e4e6c4dbdfd3e08b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cc1acc2abd202513b8469dfa1667f7e6e10443a14edcd60e4e6c4dbdfd3e08b","first_computed_at":"2026-05-17T23:54:33.991467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:33.991467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f0/blFDRgDwM0Z6N4xaiTWyQTBZ/pPAbioMO9EiqcwMiFxMocHejmauuj7Vb7iHfIEFMbnVfzYiYZoNEqGCbCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:33.992031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.11830","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:133bbf67c406054c66f189240e2f3b4b7e7303bdf3e2d76a3353da3a074ac53d","sha256:3cc02cd78b1b0332c6b2d0c7b9eeb1275d589f57ce727ef04db39e46b54fe0d8"],"state_sha256":"55cb79d7136ead7480ca38e9331b31c280dcdf9bd750da51f7079c2de57f5cd1"}